Momentum dependence of the dimensionality of the electronic states in heterostructures

Bound states of electrons (holes) in quantum wells and wires with asymmetric barriers can exist in bounded regions of two-and one-dimensional momentum space, respectively. As the corresponding momentum increases, both the disappearance (increase of dimensionality) and appearance (decrease of dimensionality) of bound states as well as the existence of a sequence of several such transformations of dimensionality are possible. In the case of anisotropic effective masses in the quantum wells and barriers, the forms of the lines of disappearance and appearance of bound states are different from the forms of the isoenergy lines. Therefore there is a finite energy interval (i.e., electron density interval) where bound states exist on only a part of an isoenergy line. The dimensionality of the states can be controlled with an electric field; this should be observable in a number of the experiments discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 2, 188–193 (25 January 1997)